The invention relates to a device for the synchronized reading of a serial medium which contains digital information in the form of a series of data words of equal lengths and synchronization words (S) which are separated each time by a corresponding number of n data words (D0-D7), said device comprising a detection device for detecting at least one correctly received synchronization word and for signalling a synchronized state in reaction thereto. A device of this kind is known from U.S. Pat. No. 4,001,693. The medium therein is a mobile radio link. The data format (n=3) is shown in FIG. 4 of said Patent Specification. The synchronization procedure is described notably in column 14, lines 31-54. The known device has two states: the synchronization is correct and the synchronization is incorrect. Two kinds of error can occur in a system of this kind. The first category of errors is the changing of the content of a bit, for example, of a synchronization word. A synchronization word can then become unrecognizable as such in given circumstances. The second category of errors is formed by the loss of a bit (of a data word or of a synchronization word) or the addition of a bit. A synchronization word can thus also become unrecognizable. However, the word synchronization may also be lost. The operation of the known device can be easily disturbed by the loss or addition of a data word bit; a comparatively long period of time is then required before the synchronized state is reached again. Particularly in given applications, for example, in home entertainment equipment (storage of video and/or audio information) it is desirable that the synchronization is restored as quickly as possible; however, the requirements imposed as regards correct reception of each data bit per se are somewhat less severe than in a data processing device.